Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Varieties with definable factor congruences
HTML articles powered by AMS MathViewer

by Pedro Sánchez Terraf and Diego J. Vaggione PDF
Trans. Amer. Math. Soc. 361 (2009), 5061-5088 Request permission

Abstract:

We study direct product representations of algebras in varieties. We collect several conditions expressing that these representations are definable in a first-order-logic sense, among them the concept of Definable Factor Congruences (DFC). The main results are that DFC is a Mal’cev property and that it is equivalent to all other conditions formulated; in particular we prove that $\mathcal {V}$ has DFC if and only if $\mathcal {V}$ has $\vec {0}$ & $\vec {1}$ and Boolean Factor Congruences. We also obtain an explicit first-order definition $\Phi$ of the kernel of the canonical projections via the terms associated to the Mal’cev condition for DFC, in such a manner that it is preserved by taking direct products and direct factors. The main tool is the use of central elements, which are a generalization of both central idempotent elements in rings with identity and neutral complemented elements in a bounded lattice.
References
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 08B05, 03C40
  • Retrieve articles in all journals with MSC (2000): 08B05, 03C40
Additional Information
  • Pedro Sánchez Terraf
  • Affiliation: CIEM — Facultad de Matemática, Astronomía y Física (Fa.M.A.F.), Universidad Nacional de Córdoba, Ciudad Universitaria, Córdoba 5000, Argentina
  • Email: sterraf@famaf.unc.edu.ar
  • Diego J. Vaggione
  • Affiliation: CIEM — Facultad de Matemática, Astronomía y Física (Fa.M.A.F.), Universidad Nacional de Córdoba, Ciudad Universitaria, Córdoba 5000, Argentina
  • Email: vaggione@mate.uncor.edu
  • Received by editor(s): December 15, 2006
  • Published electronically: May 18, 2009
  • Additional Notes: This work was supported by CONICET and SECYT-UNC
  • © Copyright 2009 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 361 (2009), 5061-5088
  • MSC (2000): Primary 08B05; Secondary 03C40
  • DOI: https://doi.org/10.1090/S0002-9947-09-04921-6
  • MathSciNet review: 2515803